English

On the convergence of greedy algorithms for initial segments of the Haar basis

Functional Analysis 2015-05-13 v1

Abstract

We consider the XX-Greedy Algorithm and the Dual Greedy Algorithm in a finite-dimensional Banach space with a strictly monotone basis as the dictionary. We show that when the dictionary is an initial segment of the Haar basis in Lp[0,1]L_p[0,1] (1<p<1 < p < \infty) then the algorithms terminate after finitely many iterations and that the number of iterations is bounded by a function of the length of the initial segment. We also prove a more general result for a class of strictly monotone bases.

Keywords

Cite

@article{arxiv.0905.3036,
  title  = {On the convergence of greedy algorithms for initial segments of the Haar basis},
  author = {S. J. Dilworth and E. Odell and Th. Schlumprecht and A. Zsak},
  journal= {arXiv preprint arXiv:0905.3036},
  year   = {2015}
}